Subgroups — C₃⋊(C₁₁⋊#157) #11924708

Order 1188.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₁₁×C₃⋊D₃	C₂	1	1	yes	maximal, characteristic
2	C₁₁⋊#157	—	3	1	no	maximal
3	C₃³×C₁₁	C₄	1	1	yes	characteristic, complemented, Hall
4	C₁₁×C₃⋊D₃	D₃	1	1	yes	characteristic
5	C₃×D₃×C₁₁	—	6	2	no	—
6	Dic₃₃	—	9	1	no	maximal
7	C₃⋊#157	—	11	1	no	maximal, Hall
8	C₃²×C₁₁	—	2	2	no	—
9	C₃²×C₁₁	—	4	2	no	—
10	C₃²×C₁₁	Dic₃	1	1	yes	characteristic, complemented
11	C₂×C₃×C₁₁	—	9	1	no	—
12	D₃×C₁₁	—	6	2	no	—
13	C₃×C₃⋊D₃	D₁₁	1	1	yes	characteristic
14	Dic₁₁	—	27	1	no	Hall
15	#157	—	33	1	no	—
16	C₃×C₁₁	—	2	2	no	—
17	C₃×C₁₁	—	4	2	no	—
18	C₃×C₁₁	#157	1	1	yes	characteristic, complemented
19	C₃³	Dic₁₁	1	1	yes	characteristic, complemented, Sylow
20	C₂×C₁₁	—	9	1	no	—
21	C₃⋊D₃	D₃₃	1	1	yes	characteristic
22	C₃×D₃	—	6	2	no	—
23	Dic₃	—	99	1	no	—
24	C₁₁	C₃⋊#157	1	1	yes	characteristic, complemented, Sylow
25	C₃²	—	2	2	no	—
26	C₃²	—	4	2	no	—
27	C₃²	Dic₃₃	1	1	yes	characteristic, complemented
28	C₂×C₃	—	9	1	no	—
29	D₃	—	6	2	no	—
30	C₄	—	297	1	no	Sylow
31	C₃	—	2	2	no	—
32	C₃	—	4	2	no	—
33	C₃	C₁₁⋊#157	1	1	yes	characteristic, complemented
34	C₂	—	9	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₃³×C₁₁	C₄
prime radical, cosocle	C₃×C₁₁×C₃⋊D₃	C₂
LCS	G ▷ C₃³×C₁₁
UCS	C₁

Splittings G = N ⋊ H with N normal; H ≅ G/N.

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.